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Calculating theoretical probabilities from a table (one event)

I can find theoretical probabilities from a table showing the possible outcomes for one event.

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Year 9

Calculating theoretical probabilities from a table (one event)

I can find theoretical probabilities from a table showing the possible outcomes for one event.

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Lesson details

Key learning points

The probability of an outcome can be found by considering a table showing all possible outcomes.
The probability of a set of outcomes can be found by considering a table showing all possible outcomes.
A table of all possible outcomes can help us find a probability, even when the outcomes are not equally likely.

Keywords

Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.
Theoretical probability - A theoretical probability is a probability based on counting the number of desired outcomes from a sample space where all individual outcomes are equally likely.
Frequency - The frequency is the number of times an event occurs; or the number of individuals (people, animals, etc) with some specific property.

Common misconception

When finding the probability of an outcome based on a frequency table, pupils may use the number of different categories as the denominator rather than the total frequency.

When strawberry flavoured sweets have a frequency of 11, it means that 11 of the sweets in the box are strawberry flavoured. The box of sweets could be visually represented with each sweet being shown by the first letter of its flavour.

The class could use one of the examples from the lesson to run a large experiment. By doing this, they could see how similar the results are to what would be expected based on their theoretical probabilities.

Teacher tip

Licence

This content is © Oak National Academy Limited (2026), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
Which numbers are not prime?

Correct answer: 1

Correct answer: 9

Q2.
Which numbers are not factors of 6?

Correct answer: 12

Correct answer: 18

Q3.
The table shows data about the number of animals in a zoo. How many animals are there in total?

Correct Answer: 26, twenty six

Q4.
What is the probability that this spinner lands on 'B'?

$${1}\over{2}$$

$${1}\over{3}$$

$${1}\over{4}$$

Correct answer: $${1}\over{5}$$

Q5.
What is the probability that this spinner lands on 'A'?

$${1}\over{2}$$

$${1}\over{4}$$

$${2}\over{3}$$

Correct answer: $${2}\over{5}$$

Q6.
A regular six sided dice is rolled. What is the probability of rolling a 5?

$${1}\over{2}$$

$${1}\over{5}$$

Correct answer: $${1}\over{6}$$

$${5}\over{6}$$

Assessment exit quiz

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6 Questions

Q1.
The table shows data about the number of animals in a zoo. An animal is selected at random. Which animal has a probability of $${5}\over{26}$$ of being chosen?

lion

Correct answer: giraffe

elephant

Q2.
A group of people were surveyed and asked which of the three places they last visited. A participant in the survey is then chosen at random. What is the probability that they responded 'museum'?

$${1}\over{3}$$

$${1}\over{18}$$

$${18}\over{27}$$

Correct answer: $${18}\over{45}$$

Q3.
The tally chart shows the number of cars in a car park of each colour. A car is chosen at random from the car park. What is the probability that it is blue?

$${1}\over{7}$$

$${1}\over{3}$$

Correct answer: $${7}\over{19}$$

$${7}\over{12}$$

Q4.
The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is odd?

$${1}\over{2}$$

$${1}\over{4}$$

$${3}\over{9}$$

$${4}\over{9}$$

Correct answer: $${5}\over{9}$$

Q5.
The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is prime?

$${1}\over{2}$$

$${1}\over{4}$$

$${3}\over{9}$$

Correct answer: $${4}\over{9}$$

$${5}\over{9}$$

Q6.
The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is an odd prime?

$${1}\over{2}$$

$${1}\over{4}$$

Correct answer: $${3}\over{9}$$

$${4}\over{9}$$

$${5}\over{9}$$

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UnitMaths / Probability: theoretical probabilities

Maths

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Calculating theoretical probabilities from a table (one event)

Calculating theoretical probabilities from a table (one event)

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.Which numbers are not prime?

Q2.Which numbers are not factors of 6?

Q3.The table shows data about the number of animals in a zoo. How many animals are there in total?

Q4.What is the probability that this spinner lands on 'B'?

Q5.What is the probability that this spinner lands on 'A'?

Q6.A regular six sided dice is rolled. What is the probability of rolling a 5?

Assessment exit quiz

6 Questions

Q1.The table shows data about the number of animals in a zoo. An animal is selected at random. Which animal has a probability of $${5}\over{26}$$ of being chosen?

Q2.A group of people were surveyed and asked which of the three places they last visited. A participant in the survey is then chosen at random. What is the probability that they responded 'museum'?

Q3.The tally chart shows the number of cars in a car park of each colour. A car is chosen at random from the car park. What is the probability that it is blue?

Q4.The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is odd?

Q5.The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is prime?

Q6.The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is an odd prime?

Lesson appears in

UnitMaths / Probability: theoretical probabilities

Maths

Q1.
Which numbers are not prime?

Q2.
Which numbers are not factors of 6?

Q3.
The table shows data about the number of animals in a zoo. How many animals are there in total?

Q4.
What is the probability that this spinner lands on 'B'?

Q5.
What is the probability that this spinner lands on 'A'?

Q6.
A regular six sided dice is rolled. What is the probability of rolling a 5?

Q1.
The table shows data about the number of animals in a zoo. An animal is selected at random. Which animal has a probability of $${5}\over{26}$$ of being chosen?

Q2.
A group of people were surveyed and asked which of the three places they last visited. A participant in the survey is then chosen at random. What is the probability that they responded 'museum'?

Q3.
The tally chart shows the number of cars in a car park of each colour. A car is chosen at random from the car park. What is the probability that it is blue?

Q4.
The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is odd?

Q5.
The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is prime?

Q6.
The table shows the possible outcomes when drawing from a deck of numbered cards. All of the outcomes are equally likely. What is the probability that the card picked is an odd prime?